Two Mathematicians in a Bunker and Existence of Pi

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Evgenii Rudnyi

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Mar 4, 2012, 7:27:05 AM3/4/12
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An experiment to perform in order to prove experimentally whether Pi
exists independently from the mind

The idea came during discussion on embryophysics list

http://groups.google.com/group/embryophysics/t/419d3c1fec30e3b5

Below there is a description of the experiment that one could think of
to check the relationships between Mathematics, Mind and Nature (the MMN
experiment). In my view this could be done as a real experiment (so this
is actually not a thought experiment) provided we find two
mathematicians who agree to sacrifice their life for science. I believe
that this should be not that difficult provided the importance of the
experiment for the modern science.

Let us take a completely isolated bunker where the experiment begins.
The initial conditions are enough so that mathematicians can comfortably
chat for awhile with each other about Pi and prove that it exists.
Eventually the oxygen in the bunker will run over and both
mathematicians die. From a viewpoint of a natural science, we have a
dynamical system that eventually comes to the equilibrium state. I
assume that at the beginning when mathematicians prove that Pi exists we
have a consequence of physical states where Pi exists indeed. If you are
in doubt, please suggest any other physical states where you say that Pi
exists. The goal of the experiment is to establish what happens with Pi
at the end when the system reaches the stationary state.

Because of experimental settings, we can neglect the interaction with
environment and I hope that this could be done even for the quantum
mechanics treatment.

Before the experiment will be perform in real, you can take your bet on
whether Pi is retained after the death of mathematicians or not.

Bruno Marchal

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Mar 4, 2012, 8:39:13 AM3/4/12
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I confess I cannot make any sense of what you say here. What do you
mean by "Pi is retained", how do you verify this (after the death of
the mathematicians)?

Also, what is the initial theory that you have to use to interpret the
experience?

I have no clue of the meaning of "I assume that at the beginning when

mathematicians prove that Pi exists we have a consequence of physical

states where Pi exists indeed". "consequence of physical states where
Pi exists" contains too many vague abuse of languages.

When mathematicians proves that Pi exists, they assume a lot (real
numbers, circles, length of enough smooth curves, set theory, etc.).

Usually, they don't prove that Pi exist, they assume that all Cauchy
sequences define some number, called "real number", and they show that
curves sufficiently smooth have a length definable by such a sequence.
Then they define Pi, by the ratio of the length of a circle with its
diameter, and build the Cauchy sequence defining it.

And also, why those two poor mathematicians have to die? Is not Earth
close enough, and the death of Archimedes enough? (assuming the rest
makes sense).

You might just be joking, perhaps.

Bruno

http://iridia.ulb.ac.be/~marchal/

Evgenii Rudnyi

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Mar 4, 2012, 11:12:43 AM3/4/12
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Bruno,

Actually it is not a joke. I guess it is my first step toward Platonia.
As I am a chemist by background, the problem might be not mathematically
correct indeed. Yet, if you could help, we could improve it in this respect.

The background is as follows. I am a chemist and I am still at the level
of what you refer to as physicalism or mechanism. Before I consider your
theorem, first I would like to understand better in my own terms what
physicalsim and mechanism mean and what are the limits. When you talk
about this, it is too fast for me.

According to a common view in natural sciences, a human being (and hence
mind) has been created during evolution. Right now however, after
following discussion here, I have a problem with mathematics along this
way. Science has been pretty successful with mathematical models in
physics, chemistry and even in biology. Yet, according to my current
view, mathematics has been created by the mankind. Thereafter I have got
suddenly a question, why mathematical models (physical laws) are working
at all to describe the Universe when there was no mind. The mathematics,
it seems, was not there at the times of Big Bang.

We cannot repeat Big Bang to understand this. According to the current
economic situation, it is highly unlikely that taxpayers are ready to
spend money on bigger and bigger particle accelerators. Hence my
proposal. If we cannot repeat Big Bang, then for a relatively small
budget we could make easily a local heat death of a small Universe with
two mathematicians and see what happens with mathematics there. In a
way, we repeat evolution in the reverse direction.

It would be nice to exclude mind out of consideration at all but as this
is impossible my goal was to reduce its role as possible. We know that
mathematics is what mathematicians do. Pi is a nice number and most of
taxpayers have heard about it. In the experiment we could allow
mathematicians to write the prove that Pi exists on a paper, it would be
even simpler. If you think that some other mathematical object would be
nicer, please make your suggestion.

So, at the beginning of the experiment we have mind (two working brains
of mathematicians) and they prove on the paper that a given mathematical
object exists. An open question to discuss is what happens with this
mathematical object at the end of the experiment.

Evgenii


On 04.03.2012 14:39 Bruno Marchal said the following:

Brian Tenneson

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Mar 4, 2012, 11:28:07 AM3/4/12
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There is an important distinction between the names and notations of mathematics and the objects of study of mathematics.  I believe the former are inventions of humans while the latter exist independently of mankind.  For example, I am saying that the symbol 0 is an invention of mankind but what is pointed to by the symbol 0 is not an invention of mankind.

I can't give you absolute proof especially when we're going to assume different things (i.e., we live in different paradigms).  One thing that gives me a clue about my conclusion is that mathematical objects will not exist any less if humanity were to go extinct.  However, arguing that is like arguing for a particular answer to a koan.

Bruno Marchal

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Mar 4, 2012, 12:48:53 PM3/4/12
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On 04 Mar 2012, at 17:12, Evgenii Rudnyi wrote:

> Bruno,
>
> Actually it is not a joke. I guess it is my first step toward
> Platonia. As I am a chemist by background, the problem might be not
> mathematically correct indeed. Yet, if you could help, we could
> improve it in this respect.
>
> The background is as follows. I am a chemist and I am still at the
> level of what you refer to as physicalism or mechanism.

Hmm... You should read more carefully the post. On the contrary I
claim, and explain, that mechanism and physicalism are incompatible.

I am aware that physicalist, naturalist and materialist tend to use
mechanism as a sort of modern way to put the mind under the rug.

You can see all what I am talking about as an explanation that not
only mechanism does not solve the mind-body problem, but on the
contrary, it leads to the falsity of physicalism and the necessity to
explain where the physical (and physicalist) *belief* come from.

Mechanism entails the negation of physicalism. That's what the UDA is
all about.

The physical reality is not the fundamental reality. The physical
reality will reappear as the way the border of the mathematical
reality looks when seen form inside, from some points of view
(actually the points of view of predicting measurement values).

I can argue that with comp, concerning the basic ontological level, it
is absolutely undecidable if there is anything more than the numbers,
that is 0, the successor of zero, the successor of the successor of
zero, ...

And every lawful thing is deducible from the laws of addition and
multiplication (that you have learn is school, and certainly apply in
chemistry).

So, with mechanism, physics is not the fundamental science. Physics
has to be reduced to digital machine (number) biology, psychology,
theology (given that non provable truth have a big role in the origin
of matter).


> Before I consider your theorem, first I would like to understand
> better in my own terms what physicalsim and mechanism mean and what
> are the limits. When you talk about this, it is too fast for me.

You have to do the thought experiment. You have to admit the
hypothesis, if only for the sake of the argument.


>
> According to a common view in natural sciences, a human being (and
> hence mind) has been created during evolution.

Something like that might be locally correct, but appears to be wrong
in the comp (digital mechanist) theory.

> Right now however, after following discussion here, I have a problem
> with mathematics along this way. Science has been pretty successful
> with mathematical models in physics, chemistry and even in biology.
> Yet, according to my current view, mathematics has been created by
> the mankind. Thereafter I have got suddenly a question, why
> mathematical models (physical laws) are working at all to describe
> the Universe when there was no mind. The mathematics, it seems, was
> not there at the times of Big Bang.

You might confuse mathematics, branch of human science, and the
possible mathematical reality.

The mathematical reality does not depend on the physical reality, and
a large part of it might no depend on the human mind.

For example the fact that 17 is prime, is a mathematical fact which
does not depend on the presence of human. It is just the fact that a
line of 17 distinguishable objects cannot be cut in a finite of part
to be reassembled into a rectangle different from the line itself. For
example 8 is not prime because the line

. . . . . . . .

can be cut and become

. . . .
. . . .

You might convince you experimentally that 17 is prime in this way,
but you can also prove it entirely as a consequence of the laws of
addition and multiplication. No concept of physics enter in this at
all. You might *apparently* need a physical reality to convince a
human being that 17 is prime, but you don't need to refer to it to
transmit the concept of prime number, despite it can helps for the
intuition, like above.

>
> We cannot repeat Big Bang to understand this.

Remember that we (try) to be scientist, meaning that we cannot commit
ourself ontologically, except by making clear our postulate. The big-
bang theory is a theory, an hypothesis, which usually assume an
ontological (primitively existing) universe.

With mechanism, that theory is already refuted by UDA+MGA.

What is the big bang, then. Open problem. Most plausibly a first
person plural sharable computational state of some universal number.

> According to the current economic situation, it is highly unlikely
> that taxpayers are ready to spend money on bigger and bigger
> particle accelerators. Hence my proposal. If we cannot repeat Big
> Bang, then for a relatively small budget we could make easily a
> local heat death of a small Universe with two mathematicians and see
> what happens with mathematics there. In a way, we repeat evolution
> in the reverse direction.

I can see you don't like mathematician!
:)

>
> It would be nice to exclude mind out of consideration at all but as
> this is impossible my goal was to reduce its role as possible. We
> know that mathematics is what mathematicians do.

Some constructivist mathematicians might agree, but most
mathematicians consider that they explore territories. They consider
that they make discoveries. Most discoveries are unexpected.
especially after Gödel, it is hard to defend a conventionalist
philosophy of math. And the, just to define what could mean
"mechanism", you need to assume that the arithmetical truth is more
primary than the mathematicians, if only to model mechanist
mathematicians by (Löbian) numbers. The you can distinguish the math
produce by the number, and the math of the number.

> Pi is a nice number


But it is a real number. I prefer to exclude them of the ontology,
because they have the same fate as matter. If they have an ontological
existence, it will not change anything in the machine (number)
epistemology. So they are like invisible horses, and with occam, you
can exclude them. Natural numbers will belief in real number,
independently of any of their ontological status.


> and most of taxpayers have heard about it. In the experiment we
> could allow mathematicians to write the prove that Pi exists on a
> paper, it would be even simpler. If you think that some other
> mathematical object would be nicer, please make your suggestion.

It is very weird, here.

>
> So, at the beginning of the experiment we have mind (two working
> brains of mathematicians) and they prove on the paper that a given
> mathematical object exists. An open question to discuss is what
> happens with this mathematical object at the end of the experiment.

Mathematical objects are invariant. Nothing happens to them. Things
can happen to them, in a relative sense, by the intermediate of true
relation bearing on them.

If you divide 8 by 4, this gives 2. But 8 remains untouched by that
operation. It is just that it is true that there exist a number which
multiplied by 4 gives 8, and that such a number is 2 (the nickname for
the successor of the successor of 0).

Mathematical object are structured only by their relations, and this
in a way which does not depend on time, space, animals, humans, or
whatever. Indeed, that is why math is useful to describe atemporally
even temporal relation, by a function of the type y = f(t).

But all questions require a precise theory in the background, and if
what I say don't help, you might think about formalizing a bit more
the background you are using.

Bruno

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Evgenii Rudnyi

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Mar 4, 2012, 3:07:32 PM3/4/12
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I understand your logic but then immediately comes a question where
mathematics objects exist. In this case Bruno is consistent when he says
that everything is formed from the mathematical objects in Platonia. Do
you mean the same?

I personally still at the position that there are some material objects,
atoms, molecules, crystals, etc., that are independent from the mind. I
believe that this is quite a typical position for natural sciences. Then
it is hard to imagine how mathematical objects coexist with physical
objects. Some sort of dualism?

Evgenii

On 04.03.2012 17:28 Brian Tenneson said the following:

John Mikes

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Mar 4, 2012, 6:17:25 PM3/4/12
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Hello, Evgenii, my fellow (former) chemist: I ended up after my 38 patents in (environmental-polymer) chemistry with an agnosticism, not 'believeing' in the atom (don't even mention 'molecules' or the macromolecules I created). It is all the figment of the human mind to EXPLAIN whatever transpired into our 'model' of presently knowables from (some?) infinite complexity - way beyond our imaginative power.
Maxim:
EVERYTHING does exist that pops up in the mind, if not otherwise: as an idea - in the mind. That is not too much help for your condition of "independently from the mind", but nothing we can 'think of' is independent from the mind. Pi is a formulatin of some effect humans found in the figment of their physical world explanations. The fact that we cannot express it in real numbers has nothing to do with its 'existence'. The 'effect did not evolve, it came with the "big Bang" (if you are a believer of it). Not with that 'retrograde history' of course, lineraly as it is drawn, reversing a postulated developmental course that is by far not 'linear'. Also: we have no proof that everything that ever showed up for us NOW is still available for us to know of.
Also it is childish to apply the mathematics of our expanded universe to the un-really concentrated energy-knot of the alleged beginning. (Physics as well). (Just think about the fairytale of the Inflation).
 
Please do not position your executable 2 scientists in the bunker before the human mind invented (discovered, as some would say) the zero. Or: writing.
Or: before the Great Greeks (Euclide, Plato, Archimedes, Aristotle etc.)
The 'setup' is by all means within my dismissal of 'thought experiments'.
IMO PI is a human formulation of something that is more than just human.
 
Regards
 
John
 


 
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Craig Weinberg

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Mar 5, 2012, 12:33:13 AM3/5/12
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On Mar 4, 3:07 pm, Evgenii Rudnyi <use...@rudnyi.ru> wrote:

>
> I personally still at the position that there are some material objects,
> atoms, molecules, crystals, etc., that are independent from the mind.

If you assume that the human mind is the only sense in the entire
cosmos then there are going to be a lot of strange conclusions that
come up. Think about the hundreds of billions of galaxies...the
billions of organisms on this planet alone.. were all of them utterly
blind and deaf to their own existence for their entire history until
the moment that Homo sapiens began to take an interest in them from
their home on this remote speck of dust?

"Thereafter I have got suddenly a question, why mathematical models
(physical laws) are working at all to describe the Universe when there
was no mind. "

It has to do with levels of perception, or what I call perceptual
inertia. Worlds. The more intelligent you are, the more worlds you can
make sense of. The more you can make sense of the motivations and
processes of lesser worlds. As the collective intelligence of our
species has concentrated the knowledge available to each of us, we
gathered meta-perceptual commonalities. Mathematical models are
actually common perception/participation strategies as characterized
by ourselves as outside observers. We are made of matter, so we see
ourselves reflected in a particular way in matter. A way which is both
intimately familiar and alien to us.

The problem is that matter is only half of the story. We are also made
of ourselves. We need mathematical models to plumb the depths of
mysteries which are beyond our own frame of reference. Mysteries that
cut across distant levels like physics and chemistry. The closer we
get to our own level of perception however, the less mathematical
models tell the whole story. Biology, zoology, anthropology,
psychology, all benefit from mathematical models to some extent, but
they fall short of modeling what it is to be alive, to be a person,
etc. Mathematics is by definition an exterior facing manipulation. It
begins by counting on our fingers - an exterior computation which
transforms part of our body to a true set of objects - generic,
recursive, controllable. Our fingers are not a mind. They are the
beginnings of the mind offloading its grunt work onto objects. It is a
way of generalizing part of ourselves to make it seem like it is not
part of ourselves.'

Right now, in the post-Enlightenment era, our success with mathematics
has been so impressive that we have begun to imagine that we ourselves
have a mathematical basis. It is a little like following the counting
of the fingers back into the brain to find where smaller and smaller
fingers are counting. If we try a sense-based model instead, there is
no problem with mathematics being both a high level symbolic
experience within a human cortex as well as indirect experiences of
low level microcosmic events or other events which can be detected and
controlled externally with physical instruments. This is what sense
does. It jumps to conclusions. It ties levels together figuratively.
We want to move our hand, and we just do it. We don't have to
consciously transduce a signal through neural and muscular fibers. We
couldn't find a muscle fiber even if we wanted to.

This is what mathematics does for us, it extends our minds
figuratively outside of our native scale of perception, so that we
can, in a way, make more of the universe part of our figurative body.
Of course, just as we control our limbs without knowing what is really
going on under the skin, we should not mistake our success with
controlling through mathematical models for understanding the truth -
particularly the truth of our own native perceptual frame, which as
much more subtle and non-mathematical potentials. It could well be the
case that introducing our external control schemas into our own world
is having increasingly toxic consequences, draining the significance
out of culture and promoting an unstoppable drone of financial
computation which consumes the whole of civilization. We may find out
that our mastery over our universe has a Sorcerer's Apprentice side
which reduces itself to an automaton even as it automates everything
around it.

Craig

Evgenii Rudnyi

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Mar 5, 2012, 6:23:21 AM3/5/12
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Bruno,

Thanks for your comments. You are right. It is necessary to be more
accurate with terms. I have read about physicalism on SEP and I see that
I do not need mechanism right now. By the way, where I can read about
mechanism? I see nothing on SEP.

Below is a new version of the problem. I have left Pi though.

Evgenii

P.S. I like a lot this quote about physicalism from SEP

"The first thing to say when considering the truth of physicalism is
that we live in an overwhelmingly physicalist or materialist
intellectual culture. The result is that, as things currently stand, the
standards of argumentation required to persuade someone of the truth of
physicalism are much lower than the standards required to persuade
someone of its negation. (The point here is a perfectly general one: if
you already believe or want something to be true, you are likely to
accept fairly low standards of argumentation for its truth.)"

I should confess that it describes my personal feeling very well. Cheers
to philosophers.

----------------------------------------------------------------
An experiment to perform in order to find experimentally what is the
meaning of Pi under the physicalism hypothesis

Version 2.0

*Assumptions*
-------------
I assume physicalism. From SEP

http://plato.stanford.edu/entries/physicalism/

"Physicalism is the thesis that everything is physical, or as
contemporary philosophers sometimes put it, that everything supervenes
on, or is necessitated by, the physical."

"The general idea is that the nature of the actual world (i.e. the
universe and everything in it) conforms to a certain condition, the
condition of being physical. Of course, physicalists don't deny that the
world might contain many items that at first glance don't seem physical
� items of a biological, or psychological, or moral, or social nature.
But they insist nevertheless that at the end of the day such items are
either physical or supervene on the physical."

"Physicalism is sometimes known as �materialism�; indeed, on one strand
to contemporary usage, the terms �physicalism� and �materialism� are
interchangeable."

*Problem*
---------
The Pi number enjoys extensive use in physics. This raises the question
what Pi means under the physicalism hypothesis.

*Experiment*
------------

Below there is a description of the experiment that one could think of

to check the relationships between Pi and physicalism.

Let us take a completely isolated bunker where the experiment begins.

There are two mathematicians in the bunker and the initial conditions
are enough so that mathematicians can comfortably work for awhile and
prove the existence of Pi on a paper. Eventually the oxygen in the

bunker will run over and both mathematicians die.

From a physicalism viewpoint, we have a dynamical system that
eventually comes to the equilibrium state. Because of experimental

settings, we can neglect the interaction with environment and I hope
that this could be done even for the quantum mechanics treatment.

The experiment takes an operational approach to what Pi means. During
the initial stage of the experiment mathematicians prove the existence
of Pi. This should be enough to claim that Pi is present in the bunker
at least for some moments.

*Questions to discuss*
----------------------

How Pi supervenes to the physical states of the bunker with mathematicians?

Is Pi invariant in respect to states of the dynamical system in question
or not?

On 04.03.2012 18:48 Bruno Marchal said the following:

> big-bang theory is a theory, an hypothesis, which usually assume an


> ontological (primitively existing) universe.
>
> With mechanism, that theory is already refuted by UDA+MGA.
>
> What is the big bang, then. Open problem. Most plausibly a first
> person plural sharable computational state of some universal number.
>
>
>
>
>
>> According to the current economic situation, it is highly unlikely
>> that taxpayers are ready to spend money on bigger and bigger
>> particle accelerators. Hence my proposal. If we cannot repeat Big
>> Bang, then for a relatively small budget we could make easily a
>> local heat death of a small Universe with two mathematicians and
>> see what happens with mathematics there. In a way, we repeat
>> evolution in the reverse direction.
>
> I can see you don't like mathematician! :)
>
>
>
>>
>> It would be nice to exclude mind out of consideration at all but as
>> this is impossible my goal was to reduce its role as possible. We
>> know that mathematics is what mathematicians do.
>
> Some constructivist mathematicians might agree, but most
> mathematicians consider that they explore territories. They consider
> that they make discoveries. Most discoveries are unexpected.

> especially after G�del, it is hard to defend a conventionalist


> philosophy of math. And the, just to define what could mean
> "mechanism", you need to assume that the arithmetical truth is more
> primary than the mathematicians, if only to model mechanist

> mathematicians by (L�bian) numbers. The you can distinguish the math

Evgenii Rudnyi

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Mar 5, 2012, 7:01:44 AM3/5/12
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John,

It is not that bad to say that we do not know something. Yet, it might
be even better to specify more accurately what exactly we do not know.

Think of your younger colleagues that do chemistry research right now.
Chemists have been quite successful and the story continues. The
concepts of atom, molecule, macromolecule, electron density, etc. have
helped a lot along this way. We may take this concepts ontologically or
just pragmatically, this is after all not that important. Materials
science seems not to be affected.

Evgenii

On 05.03.2012 00:17 John Mikes said the following:


> Hello, Evgenii, my fellow (former) chemist: I ended up after my 38
> patents in (environmental-polymer) chemistry with an agnosticism, not
> 'believeing' in the atom (don't even mention 'molecules' or the
> macromolecules I created). It is all the figment of the human mind to
> EXPLAIN whatever transpired into our 'model' of presently knowables
> from (some?) infinite complexity - way beyond our imaginative power.

> Maxim: EVERYTHING *does* exist that pops up in the mind, if not

Stephen P. King

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Mar 5, 2012, 8:34:14 AM3/5/12
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Hi Evgenii,

    This is a very fascinating statement to me and I find John's comments to be very wise! "...it might be even better to specify more accurately what exactly we do not know. " Does it not lead to a paradox? For if we could state exactly what we do not know then it would be the case that we do in fact know it and thus "we would known what we do not know", which appears to be a contradiction.
    Is this a sample of a more general kind of situation that is inevitable given the idea of self-reference? It seems to me that we need to consider that Bivalency can be a source of error sometimes, or claim that knowledge is impossible. (note the bivalence here! LOL!) I am focusing on this because it it part of my overall critique of the idea of a Theory of Everything. For example, what exactly does it mean for a sentence to have a definite truth value absent the ability to evaluate that truth value? This is what I see your hypothetical situation as discussing....

Onward!

Stephen

meekerdb

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Mar 5, 2012, 12:29:33 PM3/5/12
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On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:
The experiment takes an operational approach to what Pi means. During the initial stage of the experiment mathematicians prove the existence of Pi.

When mathematicians 'prove the existence' of something they are just showing that something which satisfies a certain definition can be inferred from a certain set of axioms.� In your example the mathematicians may define Pi as the ratio of the circumference to the diameter of a circle in Euclidean geometry. But what does that mean if geometry is not Euclidean; and we know it's not since these mathematicians are in the gravitational field of the Earth.� Mathematics is about abstract propositions.� Whether they apply to reality is a separate question.

Brent


Evgenii Rudnyi

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Mar 5, 2012, 1:03:26 PM3/5/12
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On 05.03.2012 18:29 meekerdb said the following:

> On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:
>> The experiment takes an operational approach to what Pi means.
>> During the initial stage of the experiment mathematicians prove the
>> existence of Pi.
>
> When mathematicians 'prove the existence' of something they are just
> showing that something which satisfies a certain definition can be
> inferred from a certain set of axioms. In your example the

> mathematicians may define Pi as the ratio of the circumference to the
> diameter of a circle in Euclidean geometry. But what does that mean
> if geometry is not Euclidean; and we know it's not since these
> mathematicians are in the gravitational field of the Earth.
> Mathematics is about abstract propositions. Whether they apply to

> reality is a separate question.
>
> Brent
>
>

I agree that this assumption might not be the best one. I will think it
over.

However, I do not completely understand you. How the geometry of
physical space in which mathematicians reside influences the definition
of Pi? Mathematicians will consider just Euclidean geometry, that's it.
In my view, whether the physical space Euclidean or not, does not
influence the work of mathematicians.

In any case, the problem remains. What is mathematics under the
assumption of physicalism? Do you have any idea?

Evgenii

meekerdb

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Mar 5, 2012, 1:26:55 PM3/5/12
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Exactly. Hence mathematics =/= reality.

>
> In any case, the problem remains. What is mathematics under the assumption of
> physicalism? Do you have any idea?

It's a language game.

Brent
A physicist goes off to a conference. After a week his suit�s gotten soiled and crumpled,
so he goes out to look for a dry cleaner. Walking down the main street of town, he comes
upon a store with a lot of signs out front. One of them says �Dry Cleaning.� So he goes in
with his dirty suit and asks when he can come back to pick it up. The mathematician who
owns the shop replies, �I�m terribly sorry, but we don�t do dry cleaning.� �What?�
exclaims the puzzled physicist. �The sign outside says �Dry Cleaning�!� �We do not do
anything here,� replies the mathematician. �We only sell signs!�
--- Alain Connes, in Changeux

>
> Evgenii
>

Jason Resch

unread,
Mar 5, 2012, 7:57:18 PM3/5/12
to everyth...@googlegroups.com
On Mon, Mar 5, 2012 at 12:26 PM, meekerdb <meek...@verizon.net> wrote:
On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:
On 05.03.2012 18:29 meekerdb said the following:
On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:
The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians prove the
existence of Pi.

When mathematicians 'prove the existence' of something they are just
showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to the
diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.

Brent



I agree that this assumption might not be the best one. I will think it over.

However, I do not completely understand you. How the geometry of physical space in which mathematicians reside influences the definition of Pi? Mathematicians will consider just Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, does not influence the work of mathematicians.

Exactly. Hence mathematics =/= reality.

This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale.  You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).
 



In any case, the problem remains. What is mathematics under the assumption of physicalism? Do you have any idea?

It's a language game.


This is what Hilbert proposed and what others such as Bertrand Russel tried to prove, but instead the opposite was proved in 1931.  Mathematical truth transcends the symbol manipulation game defined by any set of axioms.

Jason
 
Brent
A physicist goes off to a conference. After a week his suit’s gotten soiled and crumpled, so he goes out to look for a dry cleaner. Walking down the main street of town, he comes upon a store with a lot of signs out front. One of them says “Dry Cleaning.” So he goes in with his dirty suit and asks when he can come back to pick it up. The mathematician who owns the shop replies, “I’m terribly sorry, but we don’t do dry cleaning.” “What?” exclaims the puzzled physicist. “The sign outside says ‘Dry Cleaning’!” “We do not do anything here,” replies the mathematician. “We only sell signs!”

--- Alain Connes, in Changeux



Evgenii


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meekerdb

unread,
Mar 5, 2012, 8:24:00 PM3/5/12
to everyth...@googlegroups.com
On 3/5/2012 4:57 PM, Jason Resch wrote:
On Mon, Mar 5, 2012 at 12:26 PM, meekerdb <meek...@verizon.net> wrote:
On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:
On 05.03.2012 18:29 meekerdb said the following:
On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:
The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians prove the
existence of Pi.

When mathematicians 'prove the existence' of something they are just
showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to the
diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.

Brent



I agree that this assumption might not be the best one. I will think it over.

However, I do not completely understand you. How the geometry of physical space in which mathematicians reside influences the definition of Pi? Mathematicians will consider just Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, does not influence the work of mathematicians.

Exactly. Hence mathematics =/= reality.

This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale. �You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).

The same mathematicians in the same place could 'prove the existence' of the meeting point of parallel lines or that through a point there is more than one line parallel to a given line.� So no matter what they measure in their bunker it will be consistent with one or the other.� So you can only hold that mathematics=reality if you assume everything not self-contradictory exists in reality; but that was what the bunker thought experiment was intended to test.� You've essentially made it untestable by saying, well it may fail HERE but somewhere (Platonia?) it's really true.

Brent

�



In any case, the problem remains. What is mathematics under the assumption of physicalism? Do you have any idea?

It's a language game.


This is what Hilbert proposed and what others such as Bertrand Russel tried to prove, but instead the opposite was proved in 1931. �Mathematical truth�transcends the�symbol manipulation game defined by any set of axioms.

Jason
�
Brent

A physicist goes off to a conference. After a week his suit�s gotten soiled and crumpled, so he goes out to look for a dry cleaner. Walking down the main street of town, he comes upon a store with a lot of signs out front. One of them says �Dry Cleaning.� So he goes in with his dirty suit and asks when he can come back to pick it up. The mathematician who owns the shop replies, �I�m terribly sorry, but we don�t do dry cleaning.� �What?� exclaims the puzzled physicist. �The sign outside says �Dry Cleaning�!� �We do not do anything here,� replies the mathematician. �We only sell signs!�
--- Alain Connes, in Changeux



Evgenii


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Jason Resch

unread,
Mar 5, 2012, 11:28:33 PM3/5/12
to everyth...@googlegroups.com
On Mon, Mar 5, 2012 at 7:24 PM, meekerdb <meek...@verizon.net> wrote:
On 3/5/2012 4:57 PM, Jason Resch wrote:
On Mon, Mar 5, 2012 at 12:26 PM, meekerdb <meek...@verizon.net> wrote:
On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:
On 05.03.2012 18:29 meekerdb said the following:
On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:
The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians prove the
existence of Pi.

When mathematicians 'prove the existence' of something they are just
showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to the
diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.

Brent



I agree that this assumption might not be the best one. I will think it over.

However, I do not completely understand you. How the geometry of physical space in which mathematicians reside influences the definition of Pi? Mathematicians will consider just Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, does not influence the work of mathematicians.

Exactly. Hence mathematics =/= reality.

This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale.  You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).

The same mathematicians in the same place could 'prove the existence' of the meeting point of parallel lines or that through a point there is more than one line parallel to a given line.  So no matter what they measure in their bunker it will be consistent with one or the other.  So you can only hold that mathematics=reality if you assume everything not self-contradictory exists in reality;

Okay.
 
but that was what the bunker thought experiment was intended to test. 

I fail to see how the bunker experiment tests this.  The bunker experiment seems to assume that mathematical reality is or depends upon a physical representation.
 
You've essentially made it untestable by saying, well it may fail HERE but somewhere (Platonia?) it's really true.

People used to say Darwin's theory was untestable, because evolution was such a slow process they thought it could never be observed.  Some on this list have argued that the hypothesis has already survived one test: the unpredictability in quantum mechanics.  If instead we found our environment and observations of it to be perfectly deterministic, this would have ruled out mechanism+a single or finite universe.  Further, there is a growing collection of evidence that in most universes, conscious life is impossible.  This can also be considered as confirmation of the theory that there exists a huge diversity in structures that have existence.  Just because one proposed test will not work should not imply a theory is untestable.

A final thought: Consider what our universe would look like if you were a being outside it.  You would not be affected by the gravity of objects in our universe, for gravity only affects physical objects in this universe.  You could not see the stars or galaxies of our universe, for photons never leave it.  There would be no relativity of size, or time, or distance between your perspective and that within our universe.  You could not say what time it happened to be in our universe, or whether the world had even formed yet or long ago ended.  You could in no way make your presence known to us in this universe, for our universe is bound to follow certain fixed laws.  In summary, outside our universe there is no evidence we even exist; our entire universe is merely an abstract, immutable and timeless mathematical object.  From the outside, one could study our universe through the window of math and computer simulation, but observation through your senses or any measurement apparatus would never reveal its existence.

Jason
 

Brent

 



In any case, the problem remains. What is mathematics under the assumption of physicalism? Do you have any idea?

It's a language game.


This is what Hilbert proposed and what others such as Bertrand Russel tried to prove, but instead the opposite was proved in 1931.  Mathematical truth transcends the symbol manipulation game defined by any set of axioms.

Jason
 
Brent

A physicist goes off to a conference. After a week his suit’s gotten soiled and crumpled, so he goes out to look for a dry cleaner. Walking down the main street of town, he comes upon a store with a lot of signs out front. One of them says “Dry Cleaning.” So he goes in with his dirty suit and asks when he can come back to pick it up. The mathematician who owns the shop replies, “I’m terribly sorry, but we don’t do dry cleaning.” “What?” exclaims the puzzled physicist. “The sign outside says ‘Dry Cleaning’!” “We do not do anything here,” replies the mathematician. “We only sell signs!”
--- Alain Connes, in Changeux



Evgenii


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meekerdb

unread,
Mar 5, 2012, 11:42:27 PM3/5/12
to everyth...@googlegroups.com
On 3/5/2012 8:28 PM, Jason Resch wrote:
On Mon, Mar 5, 2012 at 7:24 PM, meekerdb <meek...@verizon.net> wrote:
On 3/5/2012 4:57 PM, Jason Resch wrote:
On Mon, Mar 5, 2012 at 12:26 PM, meekerdb <meek...@verizon.net> wrote:
On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:
On 05.03.2012 18:29 meekerdb said the following:
On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:
The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians prove the
existence of Pi.

When mathematicians 'prove the existence' of something they are just
showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to the
diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.

Brent



I agree that this assumption might not be the best one. I will think it over.

However, I do not completely understand you. How the geometry of physical space in which mathematicians reside influences the definition of Pi? Mathematicians will consider just Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, does not influence the work of mathematicians.

Exactly. Hence mathematics =/= reality.

This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale. �You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).

The same mathematicians in the same place could 'prove the existence' of the meeting point of parallel lines or that through a point there is more than one line parallel to a given line.� So no matter what they measure in their bunker it will be consistent with one or the other.� So you can only hold that mathematics=reality if you assume everything not self-contradictory exists in reality;

Okay.
�
but that was what the bunker thought experiment was intended to test.�

I fail to see how the bunker experiment tests this.� The bunker experiment seems to assume that mathematical reality is or depends upon a physical representation.
�
You've essentially made it untestable by saying, well it may fail HERE but somewhere (Platonia?) it's really true.

People used to say Darwin's theory was untestable, because evolution was such a slow process they thought it could never be observed.� Some on this list have argued that the hypothesis has already survived one test: the unpredictability in quantum mechanics.�

That specific retrodiction came from Bruno's hypothesis which is that universes are generated by computation.� What is computable is much less than all mathematics.

If instead we found our environment and observations of it to be perfectly deterministic, this would have ruled out mechanism+a single or finite universe.� Further, there is a growing collection of evidence that in most universes, conscious life is impossible.

There's a popular idea that most possible universes are inhospitable to conscious life: a theory that might well be false under Bruno's hypothesis in which consciousness and universes are both realized by computation.� In any case it doesn't warrant the conclusion that all possible universes exist.

� This can also be considered as confirmation of the theory that there exists a huge diversity in structures that have existence.� Just because one proposed test will not work should not imply a theory is untestable.

A final thought: Consider what our universe would look like if you were a being outside it.� You would not be affected by the gravity of objects in our universe, for gravity only affects physical objects in this universe.� You could not see the stars or galaxies of our universe, for photons never leave it.� There would be no relativity of size, or time, or distance between your perspective and that within our universe.� You could not say what time it happened to be in our universe, or whether the world had even formed yet or long ago ended.� You could in no way make your presence known to us in this universe, for our universe is bound to follow certain fixed laws.� In summary, outside our universe there is no evidence we even exist; our entire universe is merely an abstract, immutable and timeless mathematical object.

That's a complete non sequitur.

� From the outside, one could study our universe through the window of math and computer simulation,

I could study a mathematical or computational representation, but that's not the same as studying our universe - unless you beg the question.

Brent

Jason Resch

unread,
Mar 6, 2012, 12:34:05 AM3/6/12
to everyth...@googlegroups.com
On Mon, Mar 5, 2012 at 10:42 PM, meekerdb <meek...@verizon.net> wrote:
On 3/5/2012 8:28 PM, Jason Resch wrote:
On Mon, Mar 5, 2012 at 7:24 PM, meekerdb <meek...@verizon.net> wrote:
On 3/5/2012 4:57 PM, Jason Resch wrote:
On Mon, Mar 5, 2012 at 12:26 PM, meekerdb <meek...@verizon.net> wrote:
On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:
On 05.03.2012 18:29 meekerdb said the following:
On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:
The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians prove the
existence of Pi.

When mathematicians 'prove the existence' of something they are just
showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to the
diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.

Brent



I agree that this assumption might not be the best one. I will think it over.

However, I do not completely understand you. How the geometry of physical space in which mathematicians reside influences the definition of Pi? Mathematicians will consider just Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, does not influence the work of mathematicians.

Exactly. Hence mathematics =/= reality.

This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale.  You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).

The same mathematicians in the same place could 'prove the existence' of the meeting point of parallel lines or that through a point there is more than one line parallel to a given line.  So no matter what they measure in their bunker it will be consistent with one or the other.  So you can only hold that mathematics=reality if you assume everything not self-contradictory exists in reality;

Okay.
 
but that was what the bunker thought experiment was intended to test. 

I fail to see how the bunker experiment tests this.  The bunker experiment seems to assume that mathematical reality is or depends upon a physical representation.
 
You've essentially made it untestable by saying, well it may fail HERE but somewhere (Platonia?) it's really true.

People used to say Darwin's theory was untestable, because evolution was such a slow process they thought it could never be observed.  Some on this list have argued that the hypothesis has already survived one test: the unpredictability in quantum mechanics. 

That specific retrodiction came from Bruno's hypothesis which is that universes are generated by computation.  What is computable is much less than all mathematics.

The existence of all mathematical structures implies the existence of all programs, which is observationally indistinguishable from Bruno's result taking only the integers to exist.  I find the existence of all consistent structures to be a simpler theory.  If the integers can exist, why cant the Mandlebrot set, or the Calabi–Yau manifolds?
 


If instead we found our environment and observations of it to be perfectly deterministic, this would have ruled out mechanism+a single or finite universe.  Further, there is a growing collection of evidence that in most universes, conscious life is impossible.

There's a popular idea that most possible universes are inhospitable to conscious life: a theory that might well be false under Bruno's hypothesis in which consciousness and universes are both realized by computation. 

In Bruno's theory, "physical universes" are considered observations of minds.  Where I use the term, I refer to independent structures (both seen and unseen).
 
In any case it doesn't warrant the conclusion that all possible universes exist.


No, it doesn't prove they all exist, just that there are perhaps infinitely many universes almost exactly like this one.  Which, while not proving everything exists, is certainly something we would expect to find if indeed everything exists.

There are all these reasons and arguments that are compatible with and suggestive of the idea that all is out there.  I haven't seen one offered piece of evidence from you that would suggest the idea of mathematical reality is false.  So tell me: for what reason(s) do you reject the hypothesis?
 

  This can also be considered as confirmation of the theory that there exists a huge diversity in structures that have existence.  Just because one proposed test will not work should not imply a theory is untestable.

A final thought: Consider what our universe would look like if you were a being outside it.  You would not be affected by the gravity of objects in our universe, for gravity only affects physical objects in this universe.  You could not see the stars or galaxies of our universe, for photons never leave it.  There would be no relativity of size, or time, or distance between your perspective and that within our universe.  You could not say what time it happened to be in our universe, or whether the world had even formed yet or long ago ended.  You could in no way make your presence known to us in this universe, for our universe is bound to follow certain fixed laws.  In summary, outside our universe there is no evidence we even exist; our entire universe is merely an abstract, immutable and timeless mathematical object.

That's a complete non sequitur.
  From the outside, one could study our universe through the window of math and computer simulation,

I could study a mathematical or computational representation, but that's not the same as studying our universe - unless you beg the question.


Clearly we will not get proof of the mathematical universe hypothesis by seeing other universes and mathematical objects through telescopes.  Different universes are independent in such a way that we can only access them as we access all other mathematical structures.  Also, if your model is perfect, there should be no difference between studying the model and the object it represents.  In the future, we will be able to discover, emulate, and visit other universes by discovering them in math, and using sufficiently powerful simulations, know what it is like there, or whether or not life is possible.

That we cannot affect them from our current location does not make them any less real.  That our universe is an immutable, abstract, timeless object to a being in a different universe does not imply we are any less real, that our experiences don't matter, or that the existence of the structure that is our universe is without consequence.  Immutability says nothing about an objects reality; we cannot affect the past, or portions of our universe sufficiently far away, yet most would say these exist.  Moreover, that other universes are currently inaccessible to us does not necessarily imply that they will always be immutable and inaccessible to us.  There is always some non-zero possibility that when you wake up tomorrow, you won't find yourself in this universe, but one very far away.  The existence of all structures reconfirms, in a stronger senses, quantum immortality.  If all the other universes are out there, then given mechanism, a we are all immortal.  Unlike the immortality implied by quantum immortality, we can even survive destruction of this universe, waking up in a different one where the present one was just a very long dream.

Jason
 
Brent

meekerdb

unread,
Mar 6, 2012, 1:59:57 AM3/6/12
to everyth...@googlegroups.com
This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale. �You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).

The same mathematicians in the same place could 'prove the existence' of the meeting point of parallel lines or that through a point there is more than one line parallel to a given line.� So no matter what they measure in their bunker it will be consistent with one or the other.� So you can only hold that mathematics=reality if you assume everything not self-contradictory exists in reality;

Okay.
�
but that was what the bunker thought experiment was intended to test.�

I fail to see how the bunker experiment tests this.� The bunker experiment seems to assume that mathematical reality is or depends upon a physical representation.
�
You've essentially made it untestable by saying, well it may fail HERE but somewhere (Platonia?) it's really true.

People used to say Darwin's theory was untestable, because evolution was such a slow process they thought it could never be observed.� Some on this list have argued that the hypothesis has already survived one test: the unpredictability in quantum mechanics.�

That specific retrodiction came from Bruno's hypothesis which is that universes are generated by computation.� What is computable is much less than all mathematics.

The existence of all mathematical structures implies the existence of all programs, which is observationally indistinguishable from Bruno's result taking only the integers to exist.�

That they are observationally indistinguishable is vacuously satisfied by them both being unobservable.

I find the existence of all consistent structures to be a simpler theory.� If the integers can exist, why cant the Mandlebrot set, or the Calabi�Yau manifolds?

I didn't say that things descriable by those mathematics *can't* exist.� I just said I don't believe they do.� Yaweh *could* exist (and according to you does) but I don't believe he does.

�


If instead we found our environment and observations of it to be perfectly deterministic, this would have ruled out mechanism+a single or finite universe.� Further, there is a growing collection of evidence that in most universes, conscious life is impossible.

There's a popular idea that most possible universes are inhospitable to conscious life: a theory that might well be false under Bruno's hypothesis in which consciousness and universes are both realized by computation.�

In Bruno's theory, "physical universes" are considered observations of minds.�

Hmm? Is that right?� The UD* certainly must generate lots of programs without human-like consciousness, e.g. this universe in which dinosaurs weren't killed off.� So I'm not clear on why there wouldn't be infinitely many universes without conscious beings.


Where I use the term, I refer to independent structures (both seen and unseen).
�
In any case it doesn't warrant the conclusion that all possible universes exist.


No, it doesn't prove they all exist, just that there are perhaps infinitely many universes almost exactly like this one.�

Maybe I'm not understanding what you mean by "independent structures".� Independent of what?� I don't see that referring to independent structures has anything to do with whether they exist.


Which, while not proving everything exists, is certainly something we would expect to find if indeed everything exists.

Of course it is trivial to say that an everything theory successfully predicts the existence of what we observe to exist.� The question is whether it does the converse.� Can it predict that we don't see some (almost all) things.


There are all these reasons and arguments that are compatible with and suggestive of the idea that all is out there.� I haven't seen one offered piece of evidence from you that would suggest the idea of mathematical reality is false.� So tell me: for what reason(s) do you reject the hypothesis?

I don't reject it; I just don't accept it.� It seems to ill defined to be testable.

�

� This can also be considered as confirmation of the theory that there exists a huge diversity in structures that have existence.� Just because one proposed test will not work should not imply a theory is untestable.

A final thought: Consider what our universe would look like if you were a being outside it.� You would not be affected by the gravity of objects in our universe, for gravity only affects physical objects in this universe.� You could not see the stars or galaxies of our universe, for photons never leave it.� There would be no relativity of size, or time, or distance between your perspective and that within our universe.� You could not say what time it happened to be in our universe, or whether the world had even formed yet or long ago ended.� You could in no way make your presence known to us in this universe, for our universe is bound to follow certain fixed laws.� In summary, outside our universe there is no evidence we even exist; our entire universe is merely an abstract, immutable and timeless mathematical object.

That's a complete non sequitur.


� From the outside, one could study our universe through the window of math and computer simulation,

I could study a mathematical or computational representation, but that's not the same as studying our universe - unless you beg the question.


Clearly we will not get proof of the mathematical universe hypothesis by seeing other universes and mathematical objects through telescopes.� Different universes are independent in such a way that we can only access them as we access all other mathematical structures.�

Ask yourself WHY they are inaccessible.� Isn't it because if they were accessible then there would be contradictory facts in the world.� And why can't there be contradictory facts?� Because ex falso quodlibet.� But "quodlibet" is what has already been hypothesized. (on the other hand see Graham Priest's "In Contradiction").

Also, if your model is perfect, there should be no difference between studying the model and the object it represents.� In the future, we will be able to discover, emulate, and visit other universes by discovering them in math, and using sufficiently powerful simulations, know what it is like there, or whether or not life is possible.

Except if we are studying them or simulating them, then we can interact with them and (necessarily?) change them.


That we cannot affect them from our current location does not make them any less real.�

"Affect" and "observe" are two different things (at least classically) and if we can neither affect or observe that makes them rather like Russell's teapot.� We can't be sure it doesn't exist, but there's no reason to think it does.


That our universe is an immutable, abstract, timeless object to a being in a different universe does not imply we are any less real,

I'm not sure what being "an abstract object to a being" means, but I don't think it implies we are any more real.

that our experiences don't matter, or that the existence of the structure that is our universe is without consequence.� Immutability says nothing about an objects reality; we cannot affect the past,

Unless the past was identical with the present then something has mutated.

or portions of our universe sufficiently far away, yet most would say these exist.� Moreover, that other universes are currently inaccessible to us does not necessarily imply that they will always be immutable and inaccessible to us.� There is always some non-zero possibility that when you wake up tomorrow, you won't find yourself in this universe, but one very far away.

So you say, but I'm betting not...and so are you.

The existence of all structures reconfirms, in a stronger senses, quantum immortality.� If all the other universes are out there, then given mechanism, a we are all immortal.� Unlike the immortality implied by quantum immortality, we can even survive destruction of this universe, waking up in a different one where the present one was just a very long dream.

I'm not sure I've survived the past year.

Brent
The person I was when I was 3 years old is dead. He died because
too much new information was added to his brain.
�������� -- Saibal Mitra

acw

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>>>> deciding whale=/=whale. You can't compare one limited subset of the

>>>> whole
>>>> (such as the local part of this universe) with another subset of the
>>>> whole
>>>> (euclidean geometry), and decide that the whole (of mathematics) is
>>>> different
>>>> from the whole (of reality).
>>>
>>> The same mathematicians in the same place could 'prove the existence'
>>> of the
>>> meeting point of parallel lines or that through a point there is more
>>> than one
>>> line parallel to a given line. So no matter what they measure in
>>> their bunker
>>> it will be consistent with one or the other. So you can only hold that

>>> mathematics=reality if you assume everything not self-contradictory
>>> exists in
>>> reality;
>>>
>>>
>>> Okay.
>>>
>>> but that was what the bunker thought experiment was intended to test.
>>>
>>>
>>> I fail to see how the bunker experiment tests this. The bunker

>>> experiment seems to
>>> assume that mathematical reality is or depends upon a physical
>>> representation.
>>>
>>> You've essentially made it untestable by saying, well it may fail
>>> HERE but
>>> somewhere (Platonia?) it's really true.
>>>
>>>
>>> People used to say Darwin's theory was untestable, because evolution
>>> was such a
>>> slow process they thought it could never be observed. Some on this

>>> list have
>>> argued that the hypothesis has already survived one test: the
>>> unpredictability in
>>> quantum mechanics.
>>
>> That specific retrodiction came from Bruno's hypothesis which is that
>> universes are
>> generated by computation. What is computable is much less than all

>> mathematics.
>>
>>
>> The existence of all mathematical structures implies the existence of
>> all programs, which is observationally indistinguishable from Bruno's
>> result taking only the integers to exist.
>
> That they are observationally indistinguishable is vacuously satisfied
> by them both being unobservable.
>
>> I find the existence of all consistent structures to be a simpler
>> theory. If the integers can exist, why cant the Mandlebrot set, or the

>> Calabi�Yau manifolds?
>
> I didn't say that things descriable by those mathematics *can't* exist.
> I just said I don't believe they do. Yaweh *could* exist (and according

> to you does) but I don't believe he does.
>
Comparing everything-type theories with a random personal deity with
contradictory properties is a strawman.

>>
>>
>>> If instead we found our environment and observations of it to be
>>> perfectly
>>> deterministic, this would have ruled out mechanism+a single or finite
>>> universe. Further, there is a growing collection of evidence that in

>>> most universes,
>>> conscious life is impossible.
>>
>> There's a popular idea that most possible universes are inhospitable
>> to conscious
>> life: a theory that might well be false under Bruno's hypothesis in which
>> consciousness and universes are both realized by computation.
>>
>>
>> In Bruno's theory, "physical universes" are considered observations of
>> minds.
>
> Hmm? Is that right? The UD* certainly must generate lots of programs

> without human-like consciousness, e.g. this universe in which dinosaurs
> weren't killed off. So I'm not clear on why there wouldn't be infinitely

> many universes without conscious beings.
>
>
Dinosaurs could very well be conscious, but not self-conscious, sort of
like in-a-moment experience with very few memories or continuity.
Consciousness should not be confused with
self-awareness/self-consciousness. A mathematical object with no
conscious observer has no one to see it from the inside, thus it's
merely abstract (but for a mathematical monist or a non-eliminitavist
computationalist that would just be a program or structure empty of
observers). Of course, said structure could also find itself studied by
mathematicians, or simulated on computers or merely within other
structures (such as observer physical objects).

>> Where I use the term, I refer to independent structures (both seen and
>> unseen).
>>
>> In any case it doesn't warrant the conclusion that all possible
>> universes exist.
>>
>>
>> No, it doesn't prove they all exist, just that there are perhaps
>> infinitely many universes almost exactly like this one.
>
> Maybe I'm not understanding what you mean by "independent structures".
> Independent of what? I don't see that referring to independent

> structures has anything to do with whether they exist.
>
>> Which, while not proving everything exists, is certainly something we
>> would expect to find if indeed everything exists.
>
> Of course it is trivial to say that an everything theory successfully
> predicts the existence of what we observe to exist. The question is
> whether it does the converse. Can it predict that we don't see some
> (almost all) things.
>
I'd say that it could. A theory like COMP predicts many possibilities
outside any modern physical theories, some such things are very much
testable, but not falsifiable (because the only way we have of testing
something is by observing it and if we are part of the experiment, that
leads to tricky philosophy of science problems, which can be remedied by
thinking of reality as shared computations by a large population of
observers, not an inescapable 3p reality).

If this world was a Harry Potter magical irreducible universe or
something equally weird like purely Newtonian physics, yet with physical
(non-simulated brain), I would say that could refute COMP. Why? COMP
leads to an increase of possible continuations and so do other
everything-theories. Which essentially means that if such a theory is
true then certain types of experiences are more probable than others,
while others are utterly unlikely (but not impossible). This is yet
another way to test these types of theories.


>>
>> There are all these reasons and arguments that are compatible with and

>> suggestive of the idea that all is out there. I haven't seen one


>> offered piece of evidence from you that would suggest the idea of

>> mathematical reality is false. So tell me: for what reason(s) do you
>> reject the hypothesis?
>
> I don't reject it; I just don't accept it. It seems to ill defined to be
> testable.
>
I find it 'everything' theories more plausible than 'something' theories
- why? Ask the question "why these particlar laws of physics?" or "is
there any reason to suppose only this box in which we happen to be
exists and no other boxes which we have not observed exist?". The
'everything' theory is always simpler by Occam or other heuristics which
prefer theories of reduced complexity. The Jahweh 'theory' has way too
high complexity.

A skeptical person would not believe anything they did not experience,
but then their position would be irrealist or merely instrumental - they
refuse to try and guess what's underneath and only predict by their
experience and nothing more. A realist (but sometimes also monist or
even idealist) position would assume that something is going on
underneath and understand what it is instead of just refusing to ask
that question.

>>
>>> This can also be considered as confirmation of the theory that there
>>> exists a

>>> huge diversity in structures that have existence. Just because one


>>> proposed test
>>> will not work should not imply a theory is untestable.
>>>
>>> A final thought: Consider what our universe would look like if you
>>> were a being

>>> outside it. You would not be affected by the gravity of objects in
>>> our universe,
>>> for gravity only affects physical objects in this universe. You could
>>> not see the
>>> stars or galaxies of our universe, for photons never leave it. There


>>> would be no
>>> relativity of size, or time, or distance between your perspective and
>>> that within

>>> our universe. You could not say what time it happened to be in our
>>> universe, or
>>> whether the world had even formed yet or long ago ended. You could in


>>> no way make
>>> your presence known to us in this universe, for our universe is bound
>>> to follow

>>> certain fixed laws. In summary, outside our universe there is no


>>> evidence we even
>>> exist; our entire universe is merely an abstract, immutable and timeless
>>> mathematical object.
>>
>> That's a complete non sequitur.
>>
>>

>>> From the outside, one could study our universe through the window of
>>> math and
>>> computer simulation,
>>
>> I could study a mathematical or computational representation, but
>> that's not the
>> same as studying our universe - unless you beg the question.
>>
>>
>> Clearly we will not get proof of the mathematical universe hypothesis
>> by seeing other universes and mathematical objects through telescopes.

>> Different universes are independent in such a way that we can only
>> access them as we access all other mathematical structures.
>

> Ask yourself WHY they are inaccessible. Isn't it because if they were
> accessible then there would be contradictory facts in the world. And why
> can't there be contradictory facts? Because ex falso quodlibet. But


> "quodlibet" is what has already been hypothesized. (on the other hand
> see Graham Priest's "In Contradiction").
>
>> Also, if your model is perfect, there should be no difference between

>> studying the model and the object it represents. In the future, we


>> will be able to discover, emulate, and visit other universes by
>> discovering them in math, and using sufficiently powerful simulations,
>> know what it is like there, or whether or not life is possible.
>
> Except if we are studying them or simulating them, then we can interact
> with them and (necessarily?) change them.
>

Changing them means looking at different structure than before - either
at the structure including your changes or the structure in which you're
contained and the inner structure you're simulating.
Interacting with something means they are within the same structure.
Observing merely means simulation or inference.


>>
>> That we cannot affect them from our current location does not make
>> them any less real.
>

> "Affect" and "observe" are two different things (at least classically)
> and if we can neither affect or observe that makes them rather like

> Russell's teapot. We can't be sure it doesn't exist, but there's no


> reason to think it does.
>

There are far better reasons to consider 'everything'-type theories.
Most people don't care about theories about unicorns and ponies, but
they do care about theories about why we exist or why physics behaves
like this or that or why we have this or that experience.


>> That our universe is an immutable, abstract, timeless object to a
>> being in a different universe does not imply we are any less real,
>
> I'm not sure what being "an abstract object to a being" means, but I
> don't think it implies we are any more real.
>
>> that our experiences don't matter, or that the existence of the

>> structure that is our universe is without consequence. Immutability


>> says nothing about an objects reality; we cannot affect the past,
>
> Unless the past was identical with the present then something has mutated.
>
>> or portions of our universe sufficiently far away, yet most would say

>> these exist. Moreover, that other universes are currently inaccessible


>> to us does not necessarily imply that they will always be immutable

>> and inaccessible to us. There is always some non-zero possibility that


>> when you wake up tomorrow, you won't find yourself in this universe,
>> but one very far away.
>
> So you say, but I'm betting not...and so are you.
>

What if you find yourself in a situation which greatly reduces your
measure? I would say that would be grounds for unusual expectations.
There's also a variety of thought experiments (some eventually
realisable as actual experiments) which would let you test at least COMP
or MWI (partially).


>> The existence of all structures reconfirms, in a stronger senses,

>> quantum immortality. If all the other universes are out there, then
>> given mechanism, a we are all immortal. Unlike the immortality implied


>> by quantum immortality, we can even survive destruction of this
>> universe, waking up in a different one where the present one was just
>> a very long dream.
>
> I'm not sure I've survived the past year.
>

I would partially agree with you here (especially with the ending
quote). I don't bet on a very strong continuity myself. I change each
passing moment, and I experience discontinuity while sleeping or
otherwise being unconscious. However, as most humans we have
*expectations* and we unconsciously have such inductive beliefs in a
continuity, and we consciously predict and model some of our
experiences. Some may say that subjective probabilities are a mess and
we shouldn't do them (and thus also ignore UDA/COMP), but I believe in
my own subjective experience (I can't doubt it, although I can see why
eliminativist theories are consistent if we ignore the mind) and I do
know that I care about my future subjective experiences. If you really
want a more precise definition of what 1p-you is, imagine an infinite
directed graph where edges are Observer Moments and this 1p-'you' (or a
history) is like a partial path between 2 points (with some small
length, always losing some of the past and gaining some of the future,
like a fuzzy sliding-window). Taking the disconnected OMs view does not
make as much sense for a creature that cares about their future states
and has mostly correct local expectations (consciously known or not).

> Brent
> The person I was when I was 3 years old is dead. He died because
> too much new information was added to his brain.

> -- Saibal Mitra
>


Evgenii Rudnyi

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Mar 6, 2012, 6:22:44 AM3/6/12
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Stephen,

The life is full of paradoxes. My point was that while philosophers
cannot solve apparently simple problems (well, these problems happen not
to be simple), engineers continue doing their business successfully. How
they do it? I believe, exactly this way, they try to understand what
they do not know. Then they make trials, run tests, etc. and finally
with some luck we get a new technology. Whether the theory of everything
exists or not, happens not be essential for the success in engineering.
I do not know why.

Right now I am at the end of Beweistheorien (Proof Theories) by Prof Hoenen

http://www.podcasts.uni-freiburg.de/podcast_content?id_content=24

At the end of his course, he considers the ontological arguments where
the goal was to proof existence from pure logic. A pretty interesting
attempt. Still there is a huge gap between logic and existence and it
seems that engineers successfully fills it. Ask them, how they do it.

Evgenii

On 05.03.2012 14:34 Stephen P. King said the following:


> On 3/5/2012 7:01 AM, Evgenii Rudnyi wrote:
>> John,
>>
>> It is not that bad to say that we do not know something. Yet, it might
>> be even better to specify more accurately what exactly we do not know.
>>
>> Think of your younger colleagues that do chemistry research right now.
>> Chemists have been quite successful and the story continues. The
>> concepts of atom, molecule, macromolecule, electron density, etc. have
>> helped a lot along this way. We may take this concepts ontologically
>> or just pragmatically, this is after all not that important. Materials
>> science seems not to be affected.
>>
>> Evgenii

...

> Hi Evgenii,
>
> This is a very fascinating statement to me and I find John's comments to
> be very wise! "...it might be even better to specify more accurately
> what exactly we do not know. " Does it not lead to a paradox? For if we
> could state exactly what we do not know then it would be the case that
> we do in fact know it and thus "we would known what we do not know",
> which appears to be a contradiction.
> Is this a sample of a more general kind of situation that is inevitable
> given the idea of self-reference? It seems to me that we need to
> consider that Bivalency

> <http://en.wikipedia.org/wiki/Principle_of_bivalence> can be a source of

Bruno Marchal

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Mar 6, 2012, 7:05:24 AM3/6/12
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What most mathematicians believe is that mathematics are the laws true
in all physical universes. And physics is true in one physical universe.
But with the mechanist hypothesis, we know better: the physical laws
are invariant in all numbers' dreams, and physical universe are shared
computations. This explains also (not directly) the non sharable
truth, the contingent one, etc.
The advantage is that we can explain both quanta and qualia, without
postulating a physical, nor a mental realm, just by listening to the
machine, and not taking them for zombie.
It hurts our intuition, today, but science always do that, since its
claim that the earth is not the center of reality. With comp we can
even understand why science has to hurt machine's intuition.

So a physicalist has just to find non mechanist theory of mind, if we
want the physical universe to be ontological (existing in some primary
sense).

Bruno

http://iridia.ulb.ac.be/~marchal/

Evgenii Rudnyi

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Mar 6, 2012, 7:07:14 AM3/6/12
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Craig,

The danger to society comes not from mathematicians, rather it could
come from technologists. Recently I have read

Jaron Lanier, You Are Not a Gadget: A Manifesto

and the author shows that the society should pay more attention to what
Silicon Valley geeks are silently doing. Just one quote

"Ideals are important in the world of technology, but the mechanism by
which ideals influence events is different than in other spheres of
life. Technologists don't use persuasion to influence you - or, at
least, we don't do it very well. There are a few master communicators
among us (like Steve Jobs), but for the most part we aren't particularly
seductive."

"We make up extensions to your being, like remote eyes and ears
(web-cams and mobile phones) and expanded memory (the world of details
you can search for online). These become the structures by which you
connect to the world and other people. These structures in turn can
change how you conceive of yourself and the world. We tinker with your
philosophy by direct manipulation of your cognitive experience, not
indirectly, through argument. It takes only a tiny group of engineers to
create technology that can shape the entire future of human experience
with incredible speed. Therefore, crucial arguments about the human
relationship with technology should take place between developers and
users before such direct manipulations are designed. This book is about
those arguments."

As for sensations, I do not know. Yesterday after I have read your
email, I went to an Italian restaurant. A small dinner, actually I
wanted just a glass of good red Italian wine, but then I took also a
small plate of cheese assorti with a couple of salad leaves, pepperoni
and bread. I have enjoyed my dinner. Whether wine, bread, cheese, salad
and pepperoni have enjoyed it too, I do not know. I would not mind, if
they did.

Evgenii


On 05.03.2012 06:33 Craig Weinberg said the following:

Bruno Marchal

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Mar 6, 2012, 7:26:03 AM3/6/12
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On 05 Mar 2012, at 19:26, meekerdb wrote:

On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:
On 05.03.2012 18:29 meekerdb said the following:
On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:
The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians prove the
existence of Pi.

When mathematicians 'prove the existence' of something they are just
showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to the
diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.

Brent



I agree that this assumption might not be the best one. I will think it over.

However, I do not completely understand you. How the geometry of physical space in which mathematicians reside influences the definition of Pi? Mathematicians will consider just Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, does not influence the work of mathematicians.

Exactly. Hence mathematics =/= reality.

Right. But this does not prove that reality is not mathematical.



In any case, the problem remains. What is mathematics under the assumption of physicalism? Do you have any idea?

It's a language game.

The word "game" is so fuzzy that this says nothing at all. Game theory is a branch of mathematics.


A physicist goes off to a conference. After a week his suit’s gotten soiled and crumpled, so he goes out to look for a dry cleaner. Walking down the main street of town, he comes upon a store with a lot of signs out front. One of them says “Dry Cleaning.” So he goes in with his dirty suit and asks when he can come back to pick it up. The mathematician who owns the shop replies, “I’m terribly sorry, but we don’t do dry cleaning.” “What?” exclaims the puzzled physicist. “The sign outside says ‘Dry Cleaning’!” “We do not do anything here,” replies the mathematician. “We only sell signs!”
--- Alain Connes, in Changeux

Connes is a mathematical realist. Are you sure the joke is not from Changeux who is strongly physicalist?

Bruno


Bruno Marchal

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Mar 6, 2012, 8:21:33 AM3/6/12